1. Using Quantum Means to Understand and Estimate Relativistic Effects
报告人： 田泽华
指导老师：荆继良 教授
湖南师范大学

2. Outline Introduction Open quantum system approach
Using Geometric phase corrections to understand thermal
nature of de Sitter space-time
Optimal quantum estimation of Unruh effect
Further works

3. Relativistic Quantum Information
1. Introduction
Relativistic quantum information:
Quantum Fields
Theory
Relativity Theory .
Relativistic Quantum Information
Information Theory
Quantum
Information
Quantum Mechanics

4. Resources/Tasks of QI well known:
Motivations:
Resources/Tasks of QI well known:
How are they (entanglement, quantum correlation, quantum teleportation )
affected by Relativity?
Are effects degraded/enhanced?
Connection between QFT and QI
Unruh effect, Hawking effect, Casimir effect
New ways to create, store, transmit, process QI
Our aim here . . .
Utilizing quantum means to understand, detect and estimate relativistic effects

5. 2. Open quantum system approach
Hamiltonian:
Detector
Atom
Environment
Atom
Master equation:
Accelerated
In curved spacetime
In thermal bath
Other cases
Phys. Rev. A 79, (2009)

6. Initial state:
Evolving state:
Eigenvalues:
Eigenvectors:

7. 3. Using geometric phase corrections to understand thermal nature of de Sitter space-time
1. The Hamiltonian H(R) depends on
a set of parameters R
2. The external parameters are time
dependent, R(T)= R(0)
3. Adiabatic approximation holds
M. Berry, Proc. Roy. Soc. A 392, 45 (1984).

8. Geometric phase in an open quantum system:
Environment
Atom
Geometric phase of the two-level atom:
D. M. Tong, E. Sjoqvist, L. C. Kwek, and C. H. Oh, PRL (2004).

9. Geometric phase of a two-level atom in de Sitter spacetime
Freely falling atom:
Static atom:
N. D. Birrell and P.C. W. Davies, Quantum Fields Theory in Curved Space (Cambridge, University Press,Cambridge, England, 1982)

10. Zehua Tian and Jiliang Jing,JHEP 04. 109 (2013).
Geometric phase of a freely falling atom in de Sitter spacetime
Geometric phase:
Inertial
Thermal
Pure phase correction :
Zehua Tian and Jiliang Jing,JHEP (2013).

11. Zehua Tian and Jiliang Jing,JHEP 04. 109 (2013).
Geometric phase of a static atom in de Sitter spacetime
Proper acceleration：
Geometric phase:
Inertial
Thermal
Pure phase correction :
Zehua Tian and Jiliang Jing,JHEP (2013).

12. Conclusions

13. 4. Optimally quantum estimation of Unruh effect
Minkowski vacuum
No particles
T=a/2π
Rindler particles

14. Some questions of estimating Unruh effect:
No linear operator that acts as an observable for temperature
Unruh temperature
Directly detect?
Quantum estimation theory
Indirectly detect
(probe)
Other parameters
(1) Which is the best probe state?
(2) Which is the optimal measurement that should be performed at the output?
(3) Which is the attainable precision?
(4) Can the precision be improved?

15. Quantum estimation Optimal measurements Ultimate bounds to precision
Cramer-Rao bound (unbiased estimators)
Variance of unbiased estimators
M  number of measurements
F Fisher information
Optimal measurement  maximum Fisher information
Optimal estimator  saturation of CR inequality

16. In quantum mechanics:

18. Exact form of Fisher information
Classical:
Quantum:
SLD operator
Mix:
Pure:

19. Quantum Cramer-Rao inequality:
Optimal measurement  maximum quantum Fisher infromation
Optimal estimator  saturation of quantum CR inequality
Accelerated atom:
Correlation function:
M. G. A. Paris, International Journal of Quantum Information 7，(2009)

20. Optimally quantum estimation of Unruh effect
Fisher information based on population measurement:
Zehua Tian, Jieci Wang, Heng Fan, and Jiliang Jing, Relativistic quantum metrology in open system dynamics.

21. Optimally quantum estimation of Unruh effect
Quantum Fisher information based on all possible POVM:
Zehua Tian, Jieci Wang, Heng Fan, and Jiliang Jing, Relativistic quantum metrology in open system dynamics.

22. Quantum Fisher information:
Optimal condition:
Quantum Fisher information:
(1) best probe state?
(2) the optimal measurement?
Population measurement
(3) the attainable precision?

23. Conclusions
1. The maximum Fisher information for population measurement is obtained
when and it is independent of any initial preparations of the probe.
2. The same configuration is also corresponding to the maximum of the quantum
Fisher information, i.e., the ultimate bound allowed by quantum mechanics to
the sensitivity of the Unruh temperature estimation can be achieved based on
the population measurement.

24. 5. Further works
1. Can we distinguish different spacetime by quantum means?
2. Can the precision be improved by entanglement, quantum discord
and other quantum resources?
3. Experimentally feasible? .

25. Thank you for your attention